Preheat oven to 200 degrees. Set a wire rack on a baking sheet and place in oven.
Place polenta and 1 cup water in a medium saucepan. Cook over medium heat, whisking constantly, until thick, 5 to 6 minutes. Whisk in milk; remove from heat and set aside.
In a large bowl, whisk together flour, salt, onion powder, garlic powder, pepper, baking powder, and cayenne; whisk in polenta mixture. Add cheese; mix to combine. Add egg; mix until well combined.
Preheat a waffle iron until hot. Spray with nonstick cooking spray. Add 1/2 cup batter to waffle iron; close and cook until deep golden brown. Using an offset spatula, carefully remove hot waffle and place on wire rack in oven. Repeat process with remaining batter, spraying iron before adding batter.